Related papers: Analytical Evaluation Of An Infinite Integral Over…

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded…

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

Bessel and modified Bessel functions of imaginary order $i\nu$ ($\nu >0$) are studied. Asymptotic expansions are derived as $\nu \to \infty$ that are uniformly valid in unbounded complex domains, with error bounds provided. Coupled with…

We compute the Bessel models of irreducible representations of the finite group $GSp(4, q)$.

This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.

We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…

We prove that every irreducible, admissible representation of GSp(4,F), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided the representation is not one-dimensional. Given such a…

We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals…

In this notes we describe the center and derivations of the Infinitesimal Hecke algebra of $sl_2$ by means of elementary computations.

A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.

We consider the problem \begin{equation}\label{Eq:Abstract} (1)\;\;\;\begin{cases} S_k(D^2u)= \lambda (1-u)^q &\mbox{in }\;\; B,\\ u <0 & \mbox{in }\;\; B,\\ u=0 &\mbox{on }\partial B, \end{cases} \end{equation} where $B$ denotes the unit…

We present new asymptotic series for the Legendre and Jacobi functions of the first and second kinds in terms of Bessel functions with appropriate arguments. The results are useful in the context of scattering problems, improve on known…

In the first part, by the first author's work of 1972, an integral representation for an ultraspherical polynomial of higher index in terms of one of lower index and an infinite series was obtained. While this representation works well from…

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.

This paper gives a natural extension of Frobenius-Stickelberger formula and Kiepert formula to Abelian functions for "Purely Trigonal Curves", especially, of degree four. A description on the theory of Abelian functions for general trigonal…

We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic…

We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the…

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…

The definite integrals $ \int_{-1}^1(1-x^2)^{(\nu-1)/2}[P_\nu(x)]^3\D x$, $ \int_{-1}^1(1-x^2)^{(\nu-1)/2}[P_\nu(x)]^2P_{\nu}(-x)\D x$, $\int_{-1}^1x(1-x^2)^{(\nu-1)/2}[P_{\nu+1}(x)]^3\D x $ and…